AAG Pre-Seminar: Luigi Lombardi (Stony Brook)

Title: Generic Vanishing Phenomena

 

Abstract: In this talk I will introduce the concept of Generic Vanishing for sheaves on smooth projective varieties. Firstly I will recall the classical result of Green and Lazarsfeld for the canonical bundle. Afterwards I will present the more recent generic vanishing theorems for other special classes of sheaves, by using the framework of Fourier--Mukai functors. Finally, I will present geometric applications of generic vanishing theorems.